However, Comcast said it was still pursuing European pay-television giant
Sky
PLC, which also has been the subject of a takeover battle between Comcast and Fox. Comcast has the higher offer for the operator, in which Fox already owns a 39% stake.
Disney
DIS -1.06%
Chief Executive Robert Iger has called Sky a “crown jewel” in the deal for Fox.

Comcast’s retreat on Thursday amounts to a major victory for Mr. Iger and ends a high-stakes chess match for Fox’s entertainment assets, viewed as a means to combat a declining U.S. pay-TV market and the rise of streaming services like
Netflix Inc.

Assuming Disney wins all necessary regulatory approvals abroad—it already secured clearance from the U.S. Justice Department—it will wind up with such businesses as the Twentieth Century Fox film and TV studio, a controlling stake in streaming-video service Hulu, and international properties including Fox’s Sky stake and Star India.

“I’d like to congratulate Bob Iger and the team at Disney and commend the Murdoch family and Fox for creating such a desirable and respected company,” Comcast Chief Executive Brian Roberts said on Thursday.

Comcast executives remain focused on winning Sky, which they view as a mini-version of Comcast-NBCUniversal that could give them a boost in the global streaming race. The cable-and-entertainment giant has offered to buy Sky for £14.75 ($19.28) a share in cash, valuing the company at $34 billion, a 5% premium to the latest offer from Fox, which has been trying since 2016 to buy the rest of Sky.

Disney has indicated in regulatory filings that it is in charge of whether Fox continues pursuing Sky. Disney still hasn’t decided if it will top Comcast’s bid, people with knowledge of Disney’s thinking said, but some analysts and people close to Comcast have argued that it might be smarter to sell Fox’s Sky stake to Comcast, rather than spend tens of billions of dollars to buy a big pay-TV distributor that may not be a key part of Disney’s future.

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In either case, a move isn’t expected soon from Disney. A vote by shareholders to approve its acquisition of Fox is scheduled for July 27, and Disney wants to confirm it will be getting those assets, including the Sky stake, before making its next move, a person familiar with the matter said. Mr. Roberts has said Comcast prefers to buy 100% of Sky but would settle for a majority stake and sharing ownership with Disney.

Sky shares fell 1.5% to £15.09 each in London trading. Investors had sent the share price higher, expecting a bidding war.

Comcast’s pursuit of Fox was a struggle from the start. Fox initially struck a $52.4 billion, all-stock deal with Disney in December, snubbing Comcast’s substantially higher stock offer, citing regulatory concerns, according to a Fox regulatory filing. The move stung Comcast executives, including Mr. Roberts, who felt their efforts weren’t being taken seriously, people close to the company said.

Mr. Roberts also was up against personal dynamics. While Messrs. Murdoch and Iger have long been friends, Mr. Murdoch and his sons viewed Mr. Roberts with wariness after years of tough dealings with Comcast over TV-channel carriage fees and Hulu, which they jointly own, people familiar with the Murdochs’ thinking have said. The Murdoch family preferred to own Disney stock over Comcast’s, the people said, because they would have more power in a combined Disney-Fox, as Mr. Roberts controls one-third of Comcast’s voting power. In addition, Mr. Iger has had a rivalry with Mr. Roberts, dating back to Comcast’s hostile bid for Disney in 2004.

Comcast executives plotted for months and thought they had a path to win when a federal judge in June blessed
AT&T Inc.’s
takeover of Time Warner Inc. over the Justice Department’s objections, a sign that a Comcast-Fox deal could withstand government scrutiny. The next day, Comcast lobbed in an unsolicited $65 billion, all-cash bid for the Fox assets that was about 20% higher than the value of Disney’s original offer. After Disney came back with its latest bid the following week, Comcast reviewed its options and considered raising money from private-equity investors or strategic suitors to finance a higher bid, people close to the company said.

The challenges to Comcast grew larger. Because of an arcane provision in U.K. takeover rules, as either Disney or Comcast raised their bids for the Fox assets in the U.S., the implied value of Sky would go up—meaning Comcast would be bidding against itself with a higher Fox offer. It was a notion that caught all parties off guard, people familiar with the matter said.

Comcast’s pursuit then hit a setback after the Justice Department said last week that it would appeal the AT&T decision, which Comcast had used to rebut concerns about regulatory risk.

Comcast executives began to determine that they would have to raise their bid for Fox substantially to top a competitor that didn’t appear to be going away and capture a company whose owner didn’t appear to want Comcast to win, a person familiar with the company’s thinking said.

“It was awfully challenging, given the advantage Disney had both from a timing perspective and a regulatory perspective,” said Dennis Hersch, who used to head Davis Polk & Wardwell’s mergers-and-acquisitions practice and was a former adviser to Mr. Roberts on deals. “Sky offers an amazing platform for Comcast, and I think they understand that business much better than Disney does from their experience in the cable industry.”

Mr. Hersch dismissed the idea that Comcast would turn to other deals after losing on Fox, saying that Sky would already be a “big bite” for Comcast if it were to win that contest.